100A QUIZ 2

 1. (a) Use components to find A -2B + C as shown in the figure. (b) Sketch the resultant vector in the figure.

Solution.  We choose the coordinate system with x-axis horizontal as shown.

(a) We find the components of the resultant vector from

         Rx =  Ax -  2Bx + Cx

             =  (5)cos30° - (2)(-2)  + 0 = 8.33.

         Ry =  Ay -  2By + Cy

             = (5)sin30°  - 0 + (-3) = -0.5

         R = (Rx2  + Ry2 )1/2 = [(8.33)2 + (-0.5)2]1/2

            = 8.34.

      we find the angle from 

        tanq = Ry/Rx = (-0.5)/(8.34) = -0.00601, which gives q  = 3.4° (below  the +x-axis).

(b)

 

2. A ball is thrown horizontally with a speed of 2.5m/s. Find its velocity after 2s in the air.

Solution. 

We find the components of the ball's initial velocity from

        vx0 = v0cosq0 = (2.5m/s)cos0 = 2.5m/s;

        vy0  = 0.

We find the components of its velocity at t = 2s from

        vx = vx0 = 2.5m/s;

        vy = vx0 - gt = 0 - (9.80m/s2)(2s) = - 19.6m/s.

We find the velocity from

        v = (vx2  + vy2 )1/2 = [(2.5m/s)2 + (-19.6m/s)2]1/2 = 19.76m/s.

We find the angle from

        tanq = vy/vx = (-19.76m/s)/(2.5m/s) = -7.880, which gives q = 82.8° (below  the horizontal).